Module also offered within study programmes:
General information:
Name:
Mathematics In Geophysics
Course of study:
2015/2016
Code:
BGF-2-107-AG-s
Faculty of:
Geology, Geophysics and Environmental Protection
Study level:
Second-cycle studies
Specialty:
Applied Geophysics
Field of study:
Geophysics
Semester:
1
Profile of education:
Academic (A)
Lecture language:
English
Form and type of study:
Full-time studies
Responsible teacher:
dr Czyżewska Katarzyna (kasia@agh.edu.pl)
Academic teachers:
dr Czyżewska Katarzyna (kasia@agh.edu.pl)
dr hab. inż. Tomecka-Suchoń Sylwia (tomecka@agh.edu.pl)
Module summary

Description of learning outcomes for module
MLO code Student after module completion has the knowledge/ knows how to/is able to Connections with FLO Method of learning outcomes verification (form of completion)
Social competence
M_K001 he/she will be able to work in a group and find the solution to any given problem in the field of Engineering GF2A_W02, GF2A_U02, GF2A_K02, GF2A_K03, GF2A_K04, GF2A_U04 Activity during classes,
Project,
Scientific paper
Skills
M_U001 he/she will acquired a deep knowledge of Mathematics that will enable him/her to properly analyse the parameters of Geophysics (used) in the context of the physical properties of rock formations and in the context of various geophysical processes GF2A_W02, GF2A_K05, GF2A_U02, GF2A_W05, GF2A_K07, GF2A_U04 Examination,
Test
M_U002 he/she will be familiar with those methodologies used in Mathematics which are also used to solve the problems in the field of Geophysics GF2A_W02, GF2A_U11, GF2A_W01, GF2A_K07, GF2A_U04, GF2A_W07 Activity during classes,
Examination,
Test
M_U003 he/she will be familiar with the advanced methodologies of Mathematics and he/she will be able to apply them when analysing the experimental data GF2A_W02, GF2A_U03, GF2A_U02, GF2A_W05, GF2A_W01, GF2A_K02, GF2A_K07, GF2A_U04 Examination,
Test
M_U004 he/she will be able to carry out further independent research that will involve finding and reading literature in both Polish and English languages GF2A_W02, GF2A_K05, GF2A_K01, GF2A_U01, GF2A_K07, GF2A_U17, GF2A_U16 Activity during classes,
Examination,
Test
Knowledge
M_W001 He/she will be familiar with and will understand the advanced phenomena of physics and various and diverse geophysical processes GF2A_U02, GF2A_K01, GF2A_W01, GF2A_U01, GF2A_K02, GF2A_K07, GF2A_U04 Examination,
Test
M_W002 He/she will know and understand those advanced methodologies used in the field of Mathematics which are vital in describing and explaining the complex problems in the field of Geophysics GF2A_W02, GF2A_K08, GF2A_U02, GF2A_U01, GF2A_K02, GF2A_K03, GF2A_U04 Activity during classes,
Examination,
Test
M_W003 He/she will acquired a deep knowledge of the various methodologies used in Mathematics and their application in general and applied Geophysics GF2A_U18, GF2A_U01, GF2A_K02, GF2A_K07, GF2A_W04, GF2A_U09 Examination,
Test
FLO matrix in relation to forms of classes
MLO code Student after module completion has the knowledge/ knows how to/is able to Form of classes
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Zaj. terenowe
Zaj. warsztatowe
Others
E-learning
Social competence
M_K001 he/she will be able to work in a group and find the solution to any given problem in the field of Engineering - - - + - - - - - - -
Skills
M_U001 he/she will acquired a deep knowledge of Mathematics that will enable him/her to properly analyse the parameters of Geophysics (used) in the context of the physical properties of rock formations and in the context of various geophysical processes - - - + - - - - - - -
M_U002 he/she will be familiar with those methodologies used in Mathematics which are also used to solve the problems in the field of Geophysics + - - + - - - - - - -
M_U003 he/she will be familiar with the advanced methodologies of Mathematics and he/she will be able to apply them when analysing the experimental data - - - + - - - - - - -
M_U004 he/she will be able to carry out further independent research that will involve finding and reading literature in both Polish and English languages - - - + - - - - - - -
Knowledge
M_W001 He/she will be familiar with and will understand the advanced phenomena of physics and various and diverse geophysical processes + - - - - - - - - - -
M_W002 He/she will know and understand those advanced methodologies used in the field of Mathematics which are vital in describing and explaining the complex problems in the field of Geophysics + - - + - - - - - - -
M_W003 He/she will acquired a deep knowledge of the various methodologies used in Mathematics and their application in general and applied Geophysics + - - + - - - - - - -
Module content
Lectures:

Complex function: complex derivative, Cauchy-Riemann equations, holomorfic function, harmonic function, conformal mapping, singular points of complex function, Taylor and Laurent series, complex integral, Cauchy theorem, residuum theorem with applications, Gamma and Beta functions
Integral transforms: Fourier and Laplace transform with applications
Special ordinary differential equations: Fuchs class equations, Frobenius method, Lagrange, Bessel, confluent, Legendre equations, Sturm-Liouville problem, orthogonal polynomials, generating function, Rodriguez formula
Mathematical physics equations: initial and boundary conditions, Laplace, heat and wave equations, separation of variables for partial differential equation, boundary value problems in various symmetries: rectangular, cylindrical and spherical

Project classes:

Complex function: complex derivative, Cauchy-Riemann equations, holomorfic function, harmonic function, conformal mapping, singular points of complex function, Taylor and Laurent series, complex integral, Cauchy theorem, residuum theorem with applications, Gamma and Beta functions
Integral transforms: Fourier and Laplace transform with applications
Special ordinary differential equations: Fuchs class equations, Frobenius method, Lagrange, Bessel, confluent, Legendre equations, Sturm-Liouville problem, orthogonal polynomials, generating function, Rodriguez formula
Mathematical physics equations: initial and boundary conditions, Laplace, heat and wave equations, separation of variables for partial differential equation, boundary value problems in various symmetries: rectangular, cylindrical and spherical

Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 173 h
Module ECTS credits 6 ECTS
Examination or Final test 12 h
Participation in lectures 28 h
Participation in auditorium classes 28 h
Preparation for classes 30 h
Realization of independently performed tasks 75 h
Additional information
Method of calculating the final grade:

Evaluation: 50% seminars and 50% final exam

Prerequisites and additional requirements:

the student should obtain a ‘pass’ grade in the course in Mathematics (3 terms) and the course in Physics (2 terms)

Recommended literature and teaching resources:

1. Arfken, G.; Mathematical Methods for Physicists, New York andLondon, Academic Press 1985
2. Conway, J.B.: Functions of One Complex Variable, Springer-Verlag Berlin and Heidelberg, Co. 2001
3. Hildebrand, F.B.: Advanced Calculus for Applications, Englewood Cliffs and New Jersey, Prentice-Hall, Inc. 1964
4. Boyce, DiPrima: Elementary Differential Equations and Boundary Value Problems, John Wiley and Sons, Inc. 2009
5. Titchmarsch, E.C.: Eigenfunction Expansions Associated with Second Order Differential Equations, London, Oxford University Press 1962
6. Farrel, O.J., Ross, B.: Solved Problems: Gamma and Beta Functions, Legendre Polynomials, Bessel Functions, New Yorn, The Macmillan Co. 1963
7. Watson, G.N.: A Treatise on the Theory of Bessel Fuctions, Cambridge, Cambridge University Press 1952

Scientific publications of module course instructors related to the topic of the module:

Additional scientific publications not specified

Additional information:

None